Answer
Not parallel: (c) $ x-y+z=0$.
Work Step by Step
(c) $ x-y+z=0$. Since the normal vector to the given plane is $\langle 1,1,1 \rangle $, then for any parallel plane its normal vector must be in the direction of $\langle 1,1,1 \rangle $. However, the plane in (c) has the normal vector $\langle 1,-1,1 \rangle $, which is not in the direction of $\langle 1,1,1 \rangle $.
